Multi-Beam Design for Near-Field Extremely Large-Scale RIS-Aided Wireless Communications

As the energy-saving array composed of passive elements, reconfigurable intelligent surface (RIS) will evolve to the extremely large-scale RIS (XL-RIS) to overcome serious path loss. This change leads to the near-field propagation becoming dominant. There are some works to explore the near-field beam design via beam training. Unfortunately, due to the constant modulus constraint for XL-RIS, most of works in the near-field scenario focus on single-beam design. For massive connectivity requirement scenario, these works will face a serious loss of beam gains, resulting in a decrease in transmission rate. To solve this problem, we propose a block coordinate descent-based scheme with majorization-minimization (MM) algorithm for multi-beam design. The proposed scheme handles constant modulus constraint from two aspects. Firstly, under this constraint, the multi-beam design is an intractable non-convex quadratic programming problem. We utilize MM algorithm to solve this problem as several iterative sub-problems which are easily to be solved. Secondly, the solution space for multi-beam optimization is confined to a limited space due to this constraint, so we introduce the phases for beam gains as an extra optimizable variable to enrich the degree of freedom for optimization. Simulation results show that the proposed scheme could achieve a superior rate 50% higher than the existing schemes.